Ebola Hemorrhagic Fever
in the Republic of Congo,
from 2000 to May 6, 2003

143

128

Meningococcal Disease
in Burkina Faso,
from Jan. to April 20, 2003

7146

1058

Severe Acute Respiratory Syndrome
Worldwide, as of May 20

7919

662

Source: WHO

The next one is going to be a real doozy. You can trust me on that.
¶ 1:12 am

Tuesday, June 03, 2003

The evolution of numbers

Fun with Numbers

The numbers we all use (1, 2, 3, 4, etc.) are known as "arabic"
numbers to distinguish them from the "Roman Numerals" (I,
II, III, IV, V, VI, etc). Actually the arabs popularized these numbers
but they were originally used by the early phonecian traders to count and
keep track of their trading accounts.

Have you ever thought why ........ 1 means "one", and 2 means
"two"? The roman numerals are easy to understand but what was the logic
behind the phonecian numbers?

It's all about angles! It's the number of angles. If
one writes the numbers down (see below) on a piece of paper in their older
forms, one quickly sees why. I have marked the angles with "o"s.

No 1 has one angle.
No 2 has two angles.
No 3 has three angles.
etc.

and "O" has no angles

Interesting, isn't it?

An ancient phonecian manuscript explains this and I thought it to be fascinating
<g>.

But what's with that crazy serif on the 7, or that European stroke running
through it? Why does the 9 get an extra curl while the 6 doesn't? And surely
the 8 needs two more angles to make it look a bit more like the real thing?
While Dr Malka appears to have quite a few sound things to say about Carpal Tunnel Syndrome or
Osteoporosis, on this subject
I think I'll need to seek a second
opinion.

One can't deny that we owe a great deal to the Phoenicians, especially with
regard to their most brilliant invention, the alphabet. Furthermore, it's
not too much of a stretch to suppose that the shapes our numbers have over
time been strongly influenced by this alphabet. This influence may have operated
at more than one level. At its most obvious, from the effects of scribal juxtaposition,
the mixing of numerals and letters together on the same page leading to a
certain stylistic uniformity. But there may also have been a more indirect
one, though the influence of Greek and Semitic symbols on the scripts of
the ancient India.

In the last few centuries BC, India emerged from a dark age that had endured
since the fall of the Indus
valley civilization fifteen hundred years earlier. It was at this time
that the written word started to reappear, especially in the form of edicts
and inscriptions left by Ashok, the
great emperor of the Mauryan Empire.
These words were written in a script known as Brahmi and in amongst
its letters we find symbols to express numeric quantities which look like
this:

Even in this embryonic form it is possible to see the outlines of their future
shapes, but it is important to realise that they did not as yet comprise a
fully developed place-notation system, something which requires the symbol
zero. Instead Brahmi used special symbols to represent 10, 20, 30, 100, 1000
and so on.

The inclusion of zero or "nothing" as a numeral occurred some time around
600 AD and it transformed the Indian counting system into one that allowed
numbers to expand without end. It could achieve this remarkable feat economically
and without cumbersome
notation or need to invent more and more symbols, a feature that all previous
systems lacked. In computer parlance, the new positional system was reallyscalable.

As a slight diversion it is worth looking at how the Greeks represented numbers
at the time. Many of us are familiar with Roman numerals but what system
did the Greeks use? All of the famous classical mathematicians were Greeks,
right?

Greek mathematical notation was not positional; it utilized many symbols
and was cumbersome to work with.

The "M" is a myriad, and represents 10,000. The Greek
work is murious (uncountable, pl. murioi).
The Romans converted to this to myriad.

It has been argued that the reason why this innovation occurred in India rather
than the West was largely because of a peculiarly Indian fascination withastronomically
huge numbers.

The traditional Indian cosmology states that the universe undergoes
cyclic periods of birth, development and decay, lasting 4.32×109 years,
each of these periods is called a Kalpa or ``day of Brahma''. During each
Kalpa the universe develops by natural means and processes, and by natural
means and processes it decays; the destruction of the universe is as certain
as the death of a mouse (and equally important). Each Kalpa is divided into
1000 ``great ages'', and each great age into 4 ages; during each age humankind
deteriorates gradually (the present age will terminate in 426,902 years).
These is no final purpose towards which the universe moves, there is no progress,
only endless repetition. We do not know how the universe began, perhaps Brahma
laid it as an egg and hatched it; perhaps it is but an error or a joke of
the Maker.

This description of the universe is remarkable for the enormous numbers it
uses. The currently accepted age of the universe is about 1018 seconds and
this corresponds to about 7 Kalpas+335 great ages. A unique feature of Indian
cosmology is that no other ancient cosmology manipulates such time periods.

In the Surya Siddanta it is stated that the stars revolved around the cosmic
mountain Meru at whose summit dwell the gods. The Earth is a sphere divided
into four continents. the planets move by the action of a cosmic wind and,
in fact, the Vedic conception of nature attributes all motion to such a wind.
It was noted that the planets do not move in perfect circles and this was
attributed to ``weather forms'' whose hands were tied to the planets by ``cords
of wind''

The Brahmi script went through a continuous evolution, spawning numerous
variants, the most important of which was the Devanagari (or
sometimes simply Nagari) script. With Devanagari numerals, the 1 was rotated
by 90 degrees and had developed a serif-like loop at the top. The 2 and 3
took on their familiar shapes due to shortcuts taken by scribes, who chose
to link the parallel bars rather than lifting their pens.

Knowledge of Indian numerals spread quickly to the West. As early as 662,
Severus Sebokht, a Nestorian bishop who lived in Keneshra on the Euphrates
river, wrote:

I will omit all discussion of the science of the Indians, ...
, of their subtle discoveries in astronomy, discoveries that are more ingenious
than those of the Greeks and the Babylonians, and of their valuable methods
of calculation which surpass description. I wish only to say that this computation
is done by means of nine signs. If those who believe, because they speak
Greek, that they have arrived at the limits of science, would read the Indian
texts, they would be convinced, even if a little late in the day, that there
are others who know something of value.

However, it had to wait until the Arab conquests before the Indian numerals
began to be adopted widely and even then only very gradually. In the 11th
century, the Muslim mathematician and astronomer al-Biruni
referring to Indian numerals wrote:

Whilst we use letters for calculation according to their numerical
value, the Indians do not use letters at all for arithmetic. And just as
the shape of the letters that they use for writing is different in different
regions of their country, so the numerical symbols vary.

While the Devanagari numerals already look quite familiar to Western eyes,
in the process of adoption by the Arabs led to a stylistic split between East
and West. The Western Arabs of Morocco and Andalusia continued to use numerals
that quite closely resembled their Devanagari forebears, even as late as
the 14th century:

However in the East, the numerals evolved quite rapidly
in a different direction.

On closer examination, it can be seen that the numbers 2, 3 and 7 have become
rotated by 90 degrees but the other figures have not. One explanation for
this is that Arab scribes who write from right to left do so by turning the
paper 90 degrees so that the right hand edge is at the top. Lines are then
laid down by writing them from top to bottom in columns. It's thought that
some scribes less familiar with the Indian signs failed to rotate them correctly.

From Spain and North Africa, the Devanagari numerals passed practically without
modification to Europe and the rest is, so to speak, history...

But while migration of the Indian numerals westward was to have a dramatic
effect on later developments, it would be wrong to think that this was the
only direction of their movement.The first millennium AD was India's Golden
Age, a time when India's power and prestige were at their zenith and its culture
was being transmitted to all of its neighbours, both East and West.

Addendum: While we are on the subject of Devanagari you may find
this article about efforts to OCR Sanskrit
interesting.

Sanskrit, in which classical Indian literature was composed, is
among the world's oldest recorded languages. But putting works created over
the past 3000 years on to the web has not been easy.

Documents written in Devanagari, the script used for Sanskrit and other
South Asian languages, can be scanned as images. But optical character recognition
(OCR) software for turning Devanagari texts into digital information that
can be searched and reformatted has not been commercially available.

That has not been for lack of effort. Because Devanagari is also used
for widely spoken contemporary languages such as Hindi, several research teams
based in India are working on OCR technology to capture it.

...Since all human beings have virtually identical DNA, geneticists have to look for slight chemical variations that distinguish one population from another. One technique involves the use of "microsatellites" - short repetitive fragments of DNA whose patterns of variation differ among populations. Because microsatellites are passed from generation to generation and have a high mutation rate, they are a useful tool for estimating when two populations diverged.

In their study, the research team compared 377 microsatellite markers in DNA collected from 1,056 individuals representing 52 geographic sites in Africa, Eurasia (the Middle East, Europe, Central and South Asia), East Asia, Oceania and the Americas.

Statistical analysis of the microsatellite data revealed a close genetic relationship between two hunter-gatherer populations in sub-Saharan Africa - the Mbuti pygmies of the Congo Basin and the Khoisan (or "bushmen") of Botswana and Namibia. These two populations "may represent the oldest branch of modern humans studied here," the authors concluded.

The data revealed a genetic split between the ancestors of these hunter-gatherer populations and the ancestors of contemporary African farming people - Bantu speakers who inhabit many countries in southern Africa. "This division occurred between 70,000 and 140,000 years ago and was followed by the expansion out of Africa into Eurasia, Oceania, East Asia and the Americas - in that order," Feldman said.

This result is consistent with an earlier study in which Feldman and others analyzed the Y chromosomes of more than 1,000 men from 21 different populations. In that study, the researchers concluded that the first human migration from Africa may have occurred roughly 66,000 years ago.

Most people know little about today's Samaritans. Many believe that the name refers to an ancient Biblical race of which no vestige survives. They are often surprised to learn that the Samaritans, who accept only the Pentateuch as Holy Writ, are a vital, intelligent group with a rich history and a distinctive language and literature, practicing their own form of worship and following age-old traditions and customs.

They claim direct descent from Ephraim and Manasseh, sons of Joseph, who entered the Promised Land with Joshua and settled in the Samaria region; while their priests stem from the tribe of Levi. The Samaritans rather resent the name by which they are known; preferring to call themselves "Shamerim" --in Hebrew, guardians-- for they contend that they have guarded the original Law of Moses, keeping it pure and unadulterated down the centuries.

Their numbers are not large, and today less than five hundred are left of a great nation that is said to have been counted in hundreds of thousands --there were estimated to be over three-quarters of a million in the early part of the Christian era. About half of the remnant live on their ancestral site, close to Mount Gerizim (1), and the other half in Holon, near Tel Aviv.